DelMonte, Guidubaldo, In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata

Page concordance

< >
Scan Original
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
< >
page |< < of 207 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N127F2" type="main">
              <s id="N127F4">
                <pb xlink:href="077/01/075.jpg" pagenum="71"/>
              eſſe longitudine, quàm ſit EH. exponatur altera magnitu­
                <lb/>
              do G, quæ ad C eandem habeat proportionem, quàm habet
                <lb/>
              DE ad EH. erunt vti〈que〉 magnitudines GC inter ſe
                <expan abbr="commẽ">commen</expan>
                <lb/>
              ſurabiles. </s>
              <s id="N12808">Deinde fiat EK æqualis EH, exponaturquè ma­
                <lb/>
              gnitudo L ipſi G æqualis. </s>
              <s id="N1280C">Quoniam igitur G ad C eſt,
                <lb/>
              vt DE ad EH, ob commenſurabilitatem æ〈que〉pondera
                <arrow.to.target n="marg62"/>
                <lb/>
              G in H, & C in D. ſimiliter æ〈que〉pondera bunt magnitudi­
                <lb/>
              nes æquales GL ex æqualibus diſtantijs EK EH. Cùm igitur
                <lb/>
              C in D ipſi G in H æ〈que〉ponderet; L verò in K ipſi quo­
                <lb/>
              〈que〉 G in H æ〈que〉ponderet; eandem habebit grauitatem
                <arrow.to.target n="marg63"/>
                <lb/>
              in D, ut L in K. Quoniam autem maiorem habet propor­
                <lb/>
              tionem DE ad EH, quàm A ad C, & vt DE ad EH, ita eſt
                <lb/>
              G ad C; maiorem habebit proportionem G ad C, quàm A
                <lb/>
              ad C. ergo maior eſt G, quàm A. ac propterea magnitudo
                <arrow.to.target n="marg64"/>
                <lb/>
              minor eſt magnitudine L. poſita igitur magnitudine L in K,
                <lb/>
              & A in H, non æ〈que〉pondera bunt; & vt ę〈que〉ponderent, o­
                <lb/>
              portet, vt A in longiori ſit diſtantia, quàm ſit EH: Inęqualia
                <lb/>
              enim grauia LA ex inęqualibus diſtantijs
                <arrow.to.target n="marg65"/>
                <lb/>
              maius quidem L in minori diſtantia EK, minus verò graue
                <lb/>
              A in maiori, quàm ſit EK, hoc eſt in maiori, quàm ſit EH.
                <lb/>
              Ita〈que〉 cùm ſit C in D æ〈que〉grauis, vt L in k; longitudo,
                <lb/>
              quæ efficit, vt A æ〈que〉ponderetipſi L in K; eadem prorſus
                <lb/>
              efficiet, vt A ipſi C in D ę〈que〉ponderare poſſit. </s>
              <s id="N1283E">A verò in
                <lb/>
              maiori diſtantia, quàm EH, ipſi L in K ę〈que〉ponderat; ergo
                <lb/>
              in maiori diſtantia, quàm EH, magnitudo A ipſi C in D
                <lb/>
              ę〈que〉ponderabit. </s>
              <s id="N12846">quod demonſtrare oportebat. </s>
            </p>
            <p id="N12848" type="margin">
              <s id="N1284A">
                <margin.target id="marg62"/>
              6.
                <emph type="italics"/>
              buius.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N12853" type="margin">
              <s id="N12855">
                <margin.target id="marg63"/>
                <emph type="italics"/>
                <expan abbr="cõmunis">communis</expan>
              no
                <lb/>
              tio ſupradi
                <lb/>
              cta.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N12864" type="margin">
              <s id="N12866">
                <margin.target id="marg64"/>
              10.
                <emph type="italics"/>
              quinti.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N1286F" type="margin">
              <s id="N12871">
                <margin.target id="marg65"/>
              3.
                <emph type="italics"/>
              huius.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N1287A" type="main">
              <s id="N1287C">Hoc demonſtrato Archimedis propoſitionem de incom­
                <lb/>
              menſurabilibus magnitudinibus aliter oſtendemus hoc
                <lb/>
              pacto. </s>
            </p>
            <p id="N12882" type="head">
              <s id="N12884">ALITER.</s>
            </p>
            <p id="N12886" type="main">
              <s id="N12888">Incommenſurabiles magnitudines ex diſtantijs permuta­
                <lb/>
              tim eandem, at〈que〉 magnitudines, proportionem habenti­
                <lb/>
              bus; ę〈que〉ponderant. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum